In this study, the evolution spectrum and emission dynamics of atoms in a defect-free quasiperiodic photonic crystal are studied. Quasiperiodic photonic crystal have advantages over periodic photonic crystal in terms of abundant and strong localized modes due to the quasiperiodic and self-approximation structures of quasiperiodic photonic crystal. The localized modes exhibit extremely large local density of states and high-quality factors in the quasiperiodic photonic crystal. The frequencies of the large local density of states of the localized modes do not depend on the polarization and the position in a particular area in the quasiperiodic photonic crystals. Due to the extremely large local density of states in the defect-free quasiperiodic photonic crystal, strong coupling between the atom and the localized mode in the quasiperiodic photonic crystal can easily occur. Correspondingly, the population of the excited state displays Rabi oscillation, and the emission spectrum of the atom splits into two peaks. Moreover, the Rabi oscillation and the evolution spectrum of the dressed atom depend on the radiation linewidth.